Package com.singularsys.jep.standard

Class ImmutableComplex

java.lang.Object
com.singularsys.jep.standard.Complex
com.singularsys.jep.standard.Complex.NonPropagatingImmutableComplex
com.singularsys.jep.standard.ImmutableComplex
All Implemented Interfaces:
Serializable
public class ImmutableComplex extends Complex.NonPropagatingImmutableComplex
An Immutable version of the Complex numbers. In this class the values of complex numbers can never be changed, further any operation like conj() or add(Complex) will also return an ImmutableComplex.
Since:
Jep 4.0
See Also:

  • Field Details

    • U_ZERO

      public static final Complex U_ZERO
      Unmodifiable constant 0+0 i

    • U_ONE

      public static final Complex U_ONE
      Unmodifiable constant 1+0 i

    • U_MINUS_ONE

      public static final Complex U_MINUS_ONE
      Unmodifiable constant -1+0 i

    • U_I

      public static final Complex U_I
      Unmodifiable constant 0+1 i

    • U_MINUS_I

      public static final Complex U_MINUS_I
      Unmodifiable constant 0-1 i

  • Constructor Details

    • ImmutableComplex

      public ImmutableComplex()

    • ImmutableComplex

      public ImmutableComplex(Complex z)

    • ImmutableComplex

      public ImmutableComplex(double x, double y)

    • ImmutableComplex

      public ImmutableComplex(double x)

    • ImmutableComplex

      public ImmutableComplex(Number x)

  • Method Details

    • polarValueOf

      public static ImmutableComplex polarValueOf(Number r, Number theta)

    • neg

      public ImmutableComplex neg()
      Description copied from class: Complex
      Returns the negative value of this complex number.
      Overrides:
      neg in class Complex
      Returns:
      -(x+i y)

    • mul

      public ImmutableComplex mul(double b)
      Description copied from class: Complex
      Multiply the complex number with a double value.
      Overrides:
      mul in class Complex
      Parameters:
      b - real number to multiply by
      Returns:
      The result of the multiplication

    • add

      public ImmutableComplex add(Complex z)
      Description copied from class: Complex
      Adds the complex number with another complex value.
      Overrides:
      add in class Complex
      Parameters:
      z - complex number to add
      Returns:
      The result of the addition

    • sub

      public ImmutableComplex sub(Complex z)
      Description copied from class: Complex
      Subtracts a complex number from this
      Overrides:
      sub in class Complex
      Parameters:
      z - complex number to subtract
      Returns:
      (this) - z

    • mul

      public ImmutableComplex mul(Complex z)
      Description copied from class: Complex
      Multiply the complex number with another complex value.
      Overrides:
      mul in class Complex
      Parameters:
      z - complex number to multiply
      Returns:
      The result of the multiplication

    • div

      public ImmutableComplex div(Complex z)
      Description copied from class: Complex
      Returns the result of dividing this complex number by the parameter. Algorithm adapted from Numerical Recipes in C - The Art of Scientific Computing ISBN 0-521-43108-5
      Overrides:
      div in class Complex
      Parameters:
      z - complex number to divide by
      Returns:
      (this)/z

    • reciprocal

      public ImmutableComplex reciprocal()
      Description copied from class: Complex
      Returns the reciprocal of a complex number 1/z. This was broken in version < 4.0.
      Overrides:
      reciprocal in class Complex
      Returns:
      1/(this)

    • power

      public ImmutableComplex power(int n)
      Description copied from class: Complex
      Raise this complex to an integer power. For small power use the Complex.fastPower(int) method which does not do repeated multiplication and is generally faster. For larger power use Complex.powerI(int) which can be more accurate.
      Overrides:
      power in class Complex
      Parameters:
      n - the power
      Returns:
      (this)^n

    • powerI

      public ImmutableComplex powerI(int n)
      Description copied from class: Complex
      Raise a complex number to an integer power. Uses the polar form [r;th]^n -> [r^n;n th] and the efficient power method from Power.power(double, int) Slower than
      Overrides:
      powerI in class Complex
      Returns:

    • fastPower

      public ImmutableComplex fastPower(int n)
      Description copied from class: Complex
      Calculate integer powers by repeated multiplications. So z^5 = z*(z*z)*(z*z). This routine is generally faster but can accumulate errors for large exponents.
      Overrides:
      fastPower in class Complex
      Returns:

    • powerD

      public ImmutableComplex powerD(double exponent)
      Description copied from class: Complex
      Returns the value of this complex number raised to the power of a real component (in double precision).

      This method considers special cases where a simpler algorithm would return "ugly" results.
      For example when the expression (-1e40)^0.5 is evaluated without considering the special case, the argument of the base is the double number closest to pi. When sin and cos are used for the final evaluation of the result, the slight difference of the argument from pi causes a non-zero value for the real component of the result. Because the value of the base is so high, the error is magnified. Although the error is normal for floating point calculations, the consideration of commonly occurring special cases improves the accuracy and aesthetics of the results.

      If you know a more elegant way to solve this problem, please let me know at [email protected] .

      Testing with roots of unity show errors are typically within 128 * ulp, so |actual-result|/|actual| < 1e-13.

      Overrides:
      powerD in class Complex
      Parameters:
      exponent - exponent
      Returns:
      (this)^exponent

    • power

      public ImmutableComplex power(double exponent)
      Description copied from class: Complex
      Returns this complex number raised to a double argument. If the exponent is an integer returns Complex.power(int) otherwise calls Complex.powerD(double).
      Overrides:
      power in class Complex
      Returns:
      this^exponent

    • power

      public ImmutableComplex power(Complex exponent)
      Description copied from class: Complex
      Returns the value of this complex number raised to the power of a complex exponent If this is zero return this. If the exponent has zero imaginary part use
      Overrides:
      power in class Complex
      Parameters:
      exponent - exponent
      Returns:
      (this)^exponent

    • conj

      public ImmutableComplex conj()
      Description copied from class: Complex
      Returns the complex conjugate.
      Overrides:
      conj in class Complex
      Returns:
      (x-i y)

    • log

      public ImmutableComplex log()
      Description copied from class: Complex
      Returns the logarithm of this complex number. The real part is Math.log(this.abs()) and the complex part is this.arg(), in the range -pi .. pi.
      Overrides:
      log in class Complex
      Returns:
      ln(z) = ln(r) + i th

    • sqrt

      public ImmutableComplex sqrt()
      Description copied from class: Complex
      Calculates the square root of this object. Adapted from Numerical Recipes in C - The Art of Scientific Computing (ISBN 0-521-43108-5)
      Overrides:
      sqrt in class Complex
      Returns:
      sqrt(z)

    • sin

      public ImmutableComplex sin()
      Description copied from class: Complex
      Returns the sine of this complex number.
      Overrides:
      sin in class Complex
      Returns:
      sin(this)

    • cos

      public ImmutableComplex cos()
      Description copied from class: Complex
      Returns the cosine of this complex number.
      Overrides:
      cos in class Complex
      Returns:
      cos(this)

    • tan

      public ImmutableComplex tan()
      Description copied from class: Complex
      Returns the tangent of this complex number.
      Overrides:
      tan in class Complex
      Returns:
      tan(this)

    • asin

      public ImmutableComplex asin()
      Description copied from class: Complex
      Returns the arcsin of this complex number.
      Overrides:
      asin in class Complex
      Returns:
      asin(this)

    • acos

      public ImmutableComplex acos()
      Description copied from class: Complex
      Returns the arccos of this complex number.
      Overrides:
      acos in class Complex
      Returns:
      acos(this)

    • atan

      public ImmutableComplex atan()
      Description copied from class: Complex
      Returns the arc tangent of this complex number.
      Overrides:
      atan in class Complex
      Returns:
      atan(this)

    • sinh

      public ImmutableComplex sinh()
      Description copied from class: Complex
      Returns the hyperbolic sine of this complex number.
      Overrides:
      sinh in class Complex
      Returns:
      sinh(this)

    • cosh

      public ImmutableComplex cosh()
      Description copied from class: Complex
      Returns the hyperbolic cosine of this complex number.
      Overrides:
      cosh in class Complex
      Returns:
      cosh(this)

    • tanh

      public ImmutableComplex tanh()
      Description copied from class: Complex
      Returns the hyperbolic tangent of this complex number.
      Overrides:
      tanh in class Complex
      Returns:
      tanh(this)

    • asinh

      public ImmutableComplex asinh()
      Description copied from class: Complex
      Returns the inverse hyperbolic sine of this complex number.
      Overrides:
      asinh in class Complex
      Returns:
      asinh(this)

    • acosh

      public ImmutableComplex acosh()
      Description copied from class: Complex
      Returns the inverse hyperbolic cosine of this complex number.
      Overrides:
      acosh in class Complex
      Returns:
      acosh(this)

    • atanh

      public ImmutableComplex atanh()
      Description copied from class: Complex
      Returns the inverse hyperbolic tangent of this complex number.
      Overrides:
      atanh in class Complex
      Returns:
      atanh(this)